邻域自适应的微分变异约束分数阶粒子群优化

分数阶粒子群算法（FOPSO）是一种具有路径记忆的改进型粒子群优化算法。在多峰约束优化问题中，针对FOPSO易于早熟和依赖于初始参数的问题，文中提出了一种邻域自适应的约束分数阶粒子群优化方法（NAFPSO）。在算法中，依据进化状态来动态调整邻域拓扑从而更新粒子位置和速度，以提高可行解的全局寻优能力和收敛速度；采用带惩罚因子的罚函数约束处理技术，迫使粒子趋向可行区域；设计了微分变异策略以增加种群多样性，增强粒子逃脱局部最优的能力。用9个约束优化基准函数实验验证了NAFPSO的有效性和收敛性能，并应用于2个约束工程设计问题，结果表明，提出的算法寻优能力强、收敛快、精度高、稳定性好，可用于有效地解决复杂的约束工程设计优化问题。

Constrained fractional-order PSO with self-adaptive neighbors and differential mutators

Fractional order particle swarm optimization (FOPSO) is an improved particle swarm optimization algorithm with trajectories memory. In the multimodal constrained optimization problem, a neighborhood adaptive constrained fractional order particle swarm optimization (NAFPSO) method was proposed to solve the problem that FOPSO was easy to premature and sensitive to the initial parameters. In the algorithm, the positions and velocities of particles in the swarm were updated by the neighborhood topologies adjusted dynamically according to the evolution state of particles, so as to improve the global optimizing ability and convergence speed. Meanwhile, the penalty function with penalty factor was employed to force the particles to approach the feasible area. The differential mutation strategy was designed to increase the swarm diversity and enhance the particle ability to escape from local optimum. 9 constrained benchmarks were used to test the effectiveness and convergence performance of the proposed algorithm, and then it was applied to 2 constrained engineering design problems. Comparison analysis shows that the proposed algorithm has higher optimization ability, faster convergence, higher accuracy and better stability, and can be applied to solve complex constrained engineering design optimization problems effectively.